Question

How do you simplify `sqrt(108x^5y^8)/sqrt(6xy^5)`?

Answer 1

`3x^2sqrt(2y^3)`

Explanation:

`sqrt(108x^5y^8)/sqrt(6xy^5)=sqrt((108x^5y^8)/(6xy^5))`
`=sqrt((108/6)(x^5/x)(y^8/y^5)`
`=sqrt((18)(x^(5-1))(y^(8-5))`
`=sqrt((18)(x^4)(y^3)`
`=3x^2sqrt(2y^3)`

Answer 2

`3x^2ysqrt(2y)`

Explanation:

Each square root can be calculated separately, or because it is a division, it can be combined into a single square root.

`sqrt(108x^5y^8)/sqrt(6xy^5)` = `sqrt(18x^4y^3) = sqrt(9 xx 2x^4y^2 y )`

=`3x^2ysqrt(2y)`